**1. Introduction**

Nanofluids are a prominent topic of research. They have a wide range of applications in engineering and technology fields. Nanofluids have potential benefits in cancer therapy, drug delivery, nuclear reactors, and solar energy. Growth enrichment and convection thermal conductivity are needed during fluid flow when an outside source is essential. Nanofluids are synthesized by scattering nanoparticles in regular fluids. In addition to regular fluids, such as lubricant, oils, water, and polymer solutions, biological fluids can also be used as base fluids. A notable development in this area was investigated after the initial research by Choi [1]. Eastman et al. [2] experimentally analyzed heat transport in the presence of water-based CuO particles and ethylene-glycol-based Al2O3 particles. Since then, different researchers have discussed the features of nanofluids [3–12]. However, the use of gold nanoparticles (Au-NPs) in biomedical science is also important, and Au-NPs can be used as therapeutic agents. They are currently used as contrast and photovoltaic agents and as drug transporters. In addition, Au-NPs have many characteristics that make them suitable for use in cancer treatment. Furthermore, owing to the high atomic number of gold, Au-NPs engender heat, which can be used for photothermal therapy of tumorous glands [13,14].

Non-Newtonian fluids play an imperative role in numerous manufacturing and engineering processes, such as food processing, petroleum digging, and chemical and

**Citation:** Khan, U.; Zaib, A.; Ishak, A. Magnetic Field Effect on Sisko Fluid Flow Containing Gold Nanoparticles through a Porous Curved Surface in the Presence of Radiation and Partial Slip. *Mathematics* **2021**, *9*, 921. https://doi.org/10.3390/math9090921

Academic Editor: Mostafa Safdari Shadloo

Received: 27 January 2021 Accepted: 19 April 2021 Published: 21 April 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

biological treatment. Previously, blood was treated as a Newtonian fluid [15]; however, Thurston [16] clarified that visco-elasticity is considered a basic property of rheological blood, which indicates that human blood is non-Newtonian, depending on the visco-elastic performance of red blood cells. Several non-Newtonian fluids are treated as blood, e.g., Sisko fluid. Khan and Shahzad [17] inspected Sisko fluid flow over a stretching sheet. Munir et al. [18] extended this research by considering the bidirectional Sisko fluid flow over a stretching surface. Khan et al. explored the effects of a magnetic field and radiation on Sisko fluid flow over a bidirectional stretching sheet [19]. Eid et al. [20] used gold nanoparticles to investigate the effects of radiation on Sisko biofluid flow over a nonlinear stretching sheet. Ahmad et al. [21] numerically investigated the significance of Sisko fluid flow over a stretching curved sheet using a nanofluid and a magnetic field. Khan et al. [22] investigated 2D Sisko fluid flow impeding nanoparticles via a radially stretching/shrinking sheet under zero-flux conditions.

The effect of radiation on blood flow is considered important in biomedical science and other medical treatment techniques, especially in thermal therapeutic procedures. One effective technique commonly used for heat treatment of different body parts is infrared radiation. This method is favored in heat therapy because it is applied directly to blood capillaries in the affected regions. In addition, it is used in the treatment of bursitis, which is inflammation of the fluid-filled sacs (bursae) that lie between bone and tendon or between skin and tendon. Inoue and Kabaya [23], Kobu [24], and Nishimoto et al. [25] experimentally investigated the effects of infrared radiation on blood flow. He et al. [26] used laser irradiation to analyze oxygen transport, temperature, and blood flow in breast tumors. Prakash and Makinde [27] explored the effects of radiation on blood flow with heat transport through an artery with stenosis. Misra and Sinha investigated the effects of a magnetic field and radiation on time-dependent blood flows with heat transfer through a porous capillary in a stretching motion [28]. Khan et al. [29] used gold nanoparticles to investigate the effects of a magnetic field on radiative blood flow over a slippery surface and obtained multiple solutions. In addition, Zaib et al. investigated the effects of a magnetic field and radiation on the mixed convective flow of a tangent hyperbolic fluid over a flat, non-isothermal vertical plate [30].

The present study investigated radiative blood flow with heat transport using a Sisko fluid containing gold nanoparticles, over a porous, curved surface with a magnetic field and partial slip. The governing partial differential equations were converted to a system of ordinary differential equations before they were solved numerically via the boundary value problem of the fourth-order (bvp4c) function available in MATLAB software, which is based on the Lobatto IIIA technique. To analyze the capability of the numerical solution process, the skin friction coefficient was compared with published results. Graphical results were presented for the velocity profile, temperature distribution, skin friction, and heat transfer rate for different values of the parameters involved. To the best of our knowledge, no study has investigated flow situations with gold nanoparticles using the Sisko model with similarity solutions. The results have implications for clinical sciences, especially in thermal therapy.
